Higher-order linear differential equations with solutions having a prescribed sequence of zeros and lying in the Dirichlet space

• Autorzy: Li-Peng Xiao
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to consider the following three problems:i
(1) for a given uniformly q-separated sequence satisfying certain conditions, find a coefficient function A(z) analytic in the unit disc such that f''' + A(z)f = 0 possesses a solution having zeros precisely at the points of this sequence;
(2) find necessary and sufficient conditions for the differential equation
$f^{(k)} + A_{k-1}f^{(k-1)} + ⋯ + A₁f' + A₀f = 0$ (*)
in the unit disc to be Blaschke-oscillatory;
(3) find sufficient conditions on the analytic coefficients of the differential equation (*) for all analytic solutions to belong to the Dirichlet space 𝓓.
Our results are a generalization of some earlier results due to J. Heittokangas and J. Gröhn.

Kategorie tematyczne

• 30J10: Blaschke products
• 34M10: Oscillation, growth of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2015
• Tom: 115
• Numer: 3
• Strony: 275-295

Daty

wydano

2015

Twórcy

autor

Li-Peng Xiao

• Institute of Mathematics and Information, Jiangxi Normal University, Nanchang, 330022, China

Identyfikatory

DOI

10.4064/ap115-3-6